Question

The correct constraints for the given feasible region are ...

• A. \(x+2y-2\geq 0,3x+5y-15\geq 0,2x-3y+6\geq 0,x\geq 0,y\geq 0\)
• B. \(x+2y-2\leq 0,3x+5y-15\leq 0,2x-3y+6\leq 0,x\geq 0,y\geq 0\)
• C. \(x+2y-2\leq 0,3x+5y-15\geq 0,2x-3y+6\geq 0,x\geq 0,y\geq 0\)
• D. \(x+2y-2\geq 0,3x+5y-15\leq 0,2x-3y+6\geq 0,x\geq 0,y\geq 0\)

Hint:

Find each line's equation from its intercepts and test the origin to choose the inequality direction.

Answer 1

The Correct Option is D

Step 1: Test a Point
Take a point inside the shaded region, for example $(3,1)$.

Step 2: Evaluate Each Line
$x+2y-2=3\gt0$, $3x+5y-15=-1\lt0$, $2x-3y+6=9\gt0$.

Step 3: Compare the Options
The signs are $\geq,\ \leq,\ \geq$ for the three lines, which is only option (D).

Final Answer:
Only option (D) has the correct inequality signs. \[ \boxed{\text{(D) }x+2y-2\geq 0,\ 3x+5y-15\leq 0,\ 2x-3y+6\geq 0,\ x\geq 0,\ y\geq 0} \]